When \(m_\chi \ll T\) , in the high \(T\)  regime, the dissipative coefficient can be computed analytically expanding around the pole, \(p_0 = \omega _p \pm i \Gamma _\chi \)  [1]},
\(\Upsilon _P \simeq \frac{4 g^4 M^2}{T} \int \frac{d^3 p}{(2 \pi )^3} \frac{n_B(p_0) ( 1 + n_B(p_0)}{\Gamma _\chi \omega _p^2} \simeq \frac{4 g^4 M^2}{h^2} \cdot \frac{T^2}{m_\chi ^3} \left( 1 + \frac{1}{\sqrt{2 \pi }} \left(\frac{m_\chi }{T}\right)^{3/2} \right) e^{-m_\chi /T} \,. \) 
